208 CHEMICAL ENGINEERING 4. Size of Balls.—Balls from 1 to 7 in. in diameter are used. In a given mill the size of balls should be determined largely by the size and hardness of the ore. Best results seem to be obtained when the mill is loaded between three-tenths and two-fifths full. 5. Speed of Milk.—This is properly a direct function of the internal radius,, and is something less than the "critical" speed. The '"critical" speed of any mill is that which will make the layer of balls next to the shell cling to the latter as the mill revolves. Davis shows this to be N - ' where N = revolutions per minute and r = radius in feet. The modern practice is to operate at three-fifths to four-fifths of this speed. At four-fifths and above, the balls tend more to cascade, and the grinding is done largely by impact. At three-fifths the action is more of a rolling nature, and grinding is done by attrition. Operators are proving by decreasing the size of the feed that they may decrease the size of balls and increase the number in the mill, securing a greater grinding surface. As the power is directly proportional to the speed, the slower the mill turns, the less the power required. Also, the slower the speed the less the capacity, so a most efficient speed exists for any particular mill, and this must be determined by experiments on the ore under treatment. 6. Open and Closed Circuits.—The tendency has been to grind in closed circuit, crowding the ore through the mill, classifying, and returning the oversize. Good practice fixes this circulating load at from four to five times the feed. Closed-circuit operation tends to keep the mill up to full capacity, and is conducive to efficient working. 7. Type of Mill—Opinion is divided as to the advisability of discharging the pulp through grates or overflowing through the trunnion without any diaphragm. The diaphragm makes the mill more sensitive to overloading. 8. Size of Mill.—The tendency is to the large-diameter mill; 9-ft. mills are the largest so far used. The power requirements for ball tube mills operated at the proper speeds for best theoretical efficiencies and with various ball loads, has been calculated by Davis, and is shown in the accompanying table. These data are, of course, the result of mathematical computations and as such are correct, but in practice, some variations will be noted. The power requirements will vary in various operations. The figures shown in the table are high for general ball-mill work, but afford an intelligent guide to requirements. The proper speeds for best efficiency, also according to Davis, are shown in the appropriate table, p. 211. In tube mill grinding, it is desirable to know the exact ratio between the tube-mill classifier circuit and the original feed. Tonnage samples with this end in view are not acceptable, as it is practically impossible to determine the moisture in a pulp from a sample large enough to represent the tonnage accurately. This ratio can be determined easily from the daily screen tests.1 Let, x = Total original feed to classifier, y = Tube-mill feed (classifier sands) A = Per cent of finished size in the original feed, (This will depend on the fineness of the overflow desired) B = Per cent of finished size in tube-mill feed, C = Per cent of finished size in tube-mill discharge, and D = Per cent of finished size in classifier overflow. 1 GEO. O. DESCHLEB, Eng. and Min. Jour., April 10, 1920.